Zero-inflated gamma distribution

Density, distribution function, and random generation for the zero-inflated gamma distribution.

Usage

dzigamma(x, shape, scale, zeroprob = 0, log = FALSE)

pzigamma(q, shape, scale, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzigamma(n, shape, scale, zeroprob = 0)

Arguments

x, q

vector of quantiles

shape

positive shape parameter

scale

positive scale parameter

zeroprob

zero-inflation probability between 0 and 1.

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

n

number of random values to return

Value

dzigamma gives the density, pzigamma gives the distribution function, and rzigamma generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

$$f(x;\,\alpha,s,p_0) = p_0\,\mathbf{1}[x=0] + (1-p_0)\,f_{\mathrm{Gamma}}(x;\,\alpha,s)\,\mathbf{1}[x>0],$$ where \(p_0\) is zeroprob.

Because the continuous part places no mass at zero, zeroprob is exactly \(P(X = 0)\), and zero-inflation coincides with a hurdle model here. The two constructions only differ for discrete distributions, where the base distribution can generate zeros of its own. GAMLSS therefore calls distributions of this type zero-adjusted rather than zero-inflated, as in its ZAGA family.

Examples

x <- rzigamma(1, 1, 1, 0.5)
d <- dzigamma(x, 1, 1, 0.5)
p <- pzigamma(x, 1, 1, 0.5)